bh 2 revisited: new, extensive measurements of laser

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BH2 Revisited: New, Extensive Measurements ofLaser-Induced Fluorescence Transitions and AbInitio Calculations of Near-Spectroscopic AccuracyFumie X. SunahoriFranklin College

Mohammed GharaibehUniversity of Jordan, Jordan

Dennis J. ClouthierUniversity of Kentucky, [email protected]

Riccardo TarroniUniversità di Bologna, Italy

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Repository CitationSunahori, Fumie X.; Gharaibeh, Mohammed; Clouthier, Dennis J.; and Tarroni, Riccardo, "BH2 Revisited: New, ExtensiveMeasurements of Laser-Induced Fluorescence Transitions and Ab Initio Calculations of Near-Spectroscopic Accuracy" (2015).Chemistry Faculty Publications. 42.https://uknowledge.uky.edu/chemistry_facpub/42

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BH2 Revisited: New, Extensive Measurements of Laser-Induced Fluorescence Transitions and Ab InitioCalculations of Near-Spectroscopic Accuracy

Notes/Citation InformationPublished in The Journal of Chemical Physics, v. 142, no. 17, article 174302, p. 174302-1 through 174302-13.

Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Anyother use requires prior permission of the author and the American Institute of Physics.

The following article appeared in The Journal of Chemical Physics, v. 142, no. 17, article 174302, p. 1-13 andmay be found at http://dx.doi.org/10.1063/1.4919094

Digital Object Identifier (DOI)http://dx.doi.org/10.1063/1.4919094

This article is available at UKnowledge: https://uknowledge.uky.edu/chemistry_facpub/42

http://dx.doi.org/10.1063/1.4919094

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THE JOURNAL OF CHEMICAL PHYSICS 142, 174302 (2015)

BH2 revisited: New, extensive measurements of laser-induced fluorescencetransitions and ab initio calculations of near-spectroscopic accuracy

Fumie X. Sunahori,1 Mohammed Gharaibeh,2 Dennis J. Clouthier,3,a)

and Riccardo Tarroni41Department of Chemistry and Physics, Franklin College, Franklin, Indiana 46131, USA2Department of Chemistry, The University of Jordan, Amman 11942, Jordan3Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055, USA4Dipartimento di Chimica Industriale “Toso Montanari,” Università di Bologna, Viale Risorgimento 4,40136 Bologna, Italy

(Received 15 March 2015; accepted 15 April 2015; published online 1 May 2015)

The spectroscopy of gas phase BH2 has not been explored experimentally since the pioneering study

of Herzberg and Johns in 1967. In the present work, laser-induced fluorescence (LIF) spectra of

the A 2B1(Πu) − X 2A1 band system of 11BH2,10BH2,

11BD2, and 10BD2 have been observed for the

first time. The free radicals were “synthesized” by an electric discharge through a precursor mixture

of 0.5% diborane (B2H6 or B2D6) in high pressure argon at the exit of a pulsed valve. A total of

67 LIF bands have been measured and rotationally analyzed, 62 of them previously unobserved.

These include transitions to a wide variety of excited state bending levels, to several stretch-bend

combination levels, and to three ground state levels which gain intensity through Renner-Teller

coupling to nearby excited state levels. As an aid to vibronic assignment of the spectra, very high

level hybrid ab initio potential energy surfaces were built starting from the coupled cluster singles

and doubles with perturbative triples (CCSD(T))/aug-cc-pV5Z level of theory for this seven-electron

system. In an effort to obtain the highest possible accuracy, the potentials were corrected for core

correlation, extrapolation to the complete basis set limit, electron correlation beyond CCSD(T), and

diagonal Born-Oppenheimer effects. The spin-rovibronic states of the various isotopologues of BH2

were calculated for energies up to 22 000 cm−1 above the X (000) level without any empirical

adjustment of the potentials or fitting to experimental data. The agreement with the new LIF data

is excellent, approaching near-spectroscopic accuracy (a few cm−1) and has allowed us to understand

the complicated spin-rovibronic energy level structure even in the region of strong Renner-Teller

resonances. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4919094]

I. INTRODUCTION

Small boron-containing free radicals are intermediates in

a variety of real-world applications, including the chemical

vapor deposition (CVD) production of boron carbide1 and

boron nitride,2 doping of semiconductors,3 plasma etching

and reactive ion etching of circuit elements,4 the production

of boron-containing films,5 and the incorporation of boron

in steel,6 to name just a few. It is, therefore, important to

establish sensitive methods for detecting and characterizing

such reactive species to aid in experimental and theoretical

programs aimed at optimizing the industrial processes. Such

methods are most likely to be spectroscopic in nature, and

future studies of the transient intermediates involved will

rely on a well-established database of molecular constants,

transition frequencies, and molecular structures. In recent

years, we have been engaged in spectroscopic studies of

boron species in the gas phase, a program which has yielded

considerable new information7–14 on the BS2, HBF, HBCl,

HBBr, BF2, and F2BO free radicals. In the present work, we

a)Author to whom correspondence should be addressed. Electronic mail:[email protected]

turn our attention to BH2, a fundamental species for which

there is a dearth of information.

The first and only spectroscopic study of the BH2 free

radical in the gas phase was reported by Herzberg and Johns15

in 1967. A new absorption spectrum in the 640-870 nm region

was found in the flash photolysis of borane carbonyl (H3BCO).

The widely spaced rotational fine structure, the marked

rotational line intensity alternation, the boron isotope effects,

and the vibrational and rotational changes on deuterium

substitution all firmly established the carrier of these bands as

the BH2 free radical. BH2 is bent in the ground state and linear

in the excited state, and the observed electronic transition is

between the two components of what would be a 2Π state

at linearity. It is rather remarkable that in the intervening

almost half a century, no further experimental spectroscopic

studies of this interesting gas phase species have been reported.

Although the ESR spectrum of BH2 in a neon matrix has been

obtained,16 the microwave and infrared spectra are unknown,

and the electronic spectroscopy has not been further explored.

Despite the dearth of experimental attention, BH2, with

only seven electrons, has been fertile ground for a large

variety of theoretical studies, too numerous to discuss in

detail here. Of particular relevance to the present work are

0021-9606/2015/142(17)/174302/13/$30.00 142, 174302-1 © 2015 AIP Publishing LLC

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174302-2 Sunahori et al. J. Chem. Phys. 142, 174302 (2015)

ab initio studies of the ground and first excited state rovibronic

energy levels17–19 culminating in a very detailed calculation19

including the effect of the electronic angular momentum and

spin-orbit coupling. These calculations have been used to

correct the vibrational assignments of the bands observed

by Herzberg and Johns,15 to predict that T0 = 4203.9 cm−1

for 11BH2, and to obtain the ground and excited state restructures as r ′′ = 1.1875 Å, θ ′′ = 129.04◦, r ′ = 1.1698 Å, and

θ ′ = 180◦.In addition to these fundamental spectroscopic and

theoretical studies, there have been concerted efforts to

understand the importance of BH2 in industrial processes.

Several theoretical studies20–25 have examined aspects of

the thermodynamics, reaction pathways, intermediates and

transition states in diborane degradation in CVD, boron

carbide production, and boron nitride growth processes. In

1989, Atkinson and coworkers26 reported using intracavity

absorption spectroscopy in situ to detect BH2 during the

plasma dissociation of diborane, under conditions similar to

those employed industrially in the deposition of boron films.

Their study established, for the first time, the presence of

the BH2 reactive intermediate under CVD conditions and

highlighted its importance in such reactions.

II. EXPERIMENT

The BH2 and BD2 free radicals were produced in a

discharge free jet expansion27 using precursor mixtures of

0.5% diborane (B2H6) or fully deuterated diborane (B2D6) in

high pressure argon. The gas mixture was injected at a pressure

of 30–40 psi through the 0.8 mm orifice of a pulsed molecular

beam valve (General Valve, Series 9) into the vacuum chamber.

After a short time delay, a pulsed electric discharge was

struck between a pair of ring electrodes mounted in a

cylindrical Delrin flow channel attached to the exit to the valve,

fragmenting the precursors and producing BH2 in the process.

The radicals were cooled to low rotational temperatures

(∼10 K) by collisions downstream of the discharge. A 1.0 cm

long, 4 mm inner diameter reheat tube28 was attached to the

exit of the discharge flow channel to increase the number of

collisions which both enhanced the production of the radicals

and suppressed the background glow from electronically

excited argon atoms.

Low-resolution laser-induced fluorescence (LIF) spectra

were recorded by exciting the jet-cooled radicals with the

collimated beam of a pulsed tunable dye laser (Lumonics

HD-500, linewidth 0.1 cm−1) and imaging the resulting

fluorescence signals onto the photocathode of a high gain

photomultiplier (EMI 9816QB). The signals were sampled

with a gated integrator and recorded with LabVIEW–based

data acquisition software. The spectra were calibrated with

optogalvanic lines from neon- and argon-filled hollow cathode

lamps to an accuracy of ∼0.1 cm−1.

The LIF spectra of 10BH2 and 10BD2 were often over-

lapped by bands of the stronger 11B isotopologues. To

circumvent these problems, we used the LIF synchronous

scanning (sync-scan) technique described previously.14 In

this method, the fluorescence is dispersed by a scanning

monochromator which is fixed on a prominent emission band

of the isotopologue(s) of interest. The excitation laser and the

monochromator are scanned synchronously under computer

control so that the resulting spectrum exhibits only those

transitions that emit down to the chosen level, focusing on

the spectrum of a subset of the molecular isotopologues and

minimizing impurity emission.

High resolution sync-scan LIF spectra were obtained in

the same fashion but using a dye laser equipped with an intra-

cavity angle-tuned etalon (Scanmate 2E), providing tunable

radiation with a linewidth of 0.035 cm−1. All high resolution

spectra were calibrated with iodine LIF transitions.29

Diborane (B2H6) and fully deuterated diborane (B2D6)

were synthesized by the reaction of sodium borohydride

(NaBH4 or NaBD4) with phosphoric acid (H3PO4 or D3PO4)

using the standard literature method.30

III. EXPERIMENTAL RESULTS AND ANALYSIS

A. Preliminary considerations

As originally shown by Herzberg and Johns,15 BH2 is

a bent near-prolate asymmetric top in the ground state, and

the first electronic transition is 2B1(Πu) − 2A1, which follows

c-type rotational selection rules. The presence of two equiv-

alent hydrogen nuclei necessitates a 3:1 [eo, oe:ee,oo] (BD2

=2:1 [ee,oo:eo,oe]) nuclear statistical weight alternation in

the populations of the lower state levels of BH2. We label the

energy levels of both states by the asymmetric top quantum

numbers NKaKc in the absence of resolvable electron spin

splittings. In the upper linear state, K ′a designates the value of

l ′ while the two values of K ′c distinguish the l-type doubling

components. In those instances where the spin splittings are

resolved, the rotational levels are designated by J, the quantum

number for the total rotational plus spin angular momentum:

J = N + 1/2(F1) and J = N − 1/2(F2). The vibrations of BH2

are labeled ν1(a1) = BH symmetric stretch, ν2(a1) = bend, and

ν3(b2) BH antisymmetric stretch.

Fig. 1 shows a schematic correlation diagram between the

energy levels of the linear excited state and the bent ground

state of BH2. Starting from the left hand side of Fig. 1,

the energy levels of a linear molecule in a 1Π state with

vibronic angular momentum quantum number K = | ± Λ ± l |are represented. The inclusion of non-zero spin-orbit coupling

further splits the vibronic levels of a 2Π state into levels labeled

by the term symbols 2S+1KP, where P = | ± Ω ± l | = | ± K± Σ |. In the BH2 case, bending of the molecular frame splits

the degenerate 2Π potential into two components, an upper one

with a single minimum at 180◦ and a lower double minimum

potential with an equilibrium HBH angle near 129◦. The right

hand side of Fig. 1 shows the energy levels for the excited

linear state (upper panel) and the bent ground state (lower

panel) and their correlations with the energy levels of the linear2Π state.31 It is found that for each group of linear Π state

vibronic levels with the same bending vibrational quantum

number, the uppermost levels with K ≤ v2 − 1 correlate with

vibronic levels of the linear excited state, while the other

vibronic levels correlate with vibrational and rotational levels

of the bent 2A1 ground state. It is apparent from Fig. 1 that

the v2 = 0 (K = 1) levels of the linear molecule correlate with



FIG. 1. Schematic diagram of the

bending levels of an AB2 triatomic

molecule. The left hand side depicts the

energy levels of a molecule in a 1Π or2Π state in the limit of small vibronic

interaction. The right hand side depicts

the corresponding energy levels of a

molecule with a large vibronic interac-

tion, such that the lower potential curve

has a minimum at a nonlinear geometry.

The correlation between the energy lev-

els in the strictly linear and linear/bent

cases is given.

the v2 = 0, Ka = 1 levels of the bent 2A1 state. As a result,

the upper (linear) state does not have a v2 = 0 level, but

rather commences with a v2 = 1, K = 0, Σ level, and there

is an alternation with the v2 = odd levels having Σ, Δ, . . .symmetry (K = even values) and v2 = even levels having Π,

Φ, . . . symmetry (K = odd values). We denote the lower state

bending levels by the v2 quantum number appropriate for the

bent molecule and the upper state levels by the v2 appropriate

for a linear molecule.19

In a 1A1 ground state, the bending levels (v2 = 0,1,2, . . .)have the rotational levels of an asymmetric top, labeled by

JKaKc, although only the Ka stacks are shown in Fig. 1. A

single unpaired electron generates a 2A1 state whose rotational

energy levels exhibit further spin splittings.

B. Medium resolution LIF spectra

Relatively intense LIF spectra of BH2 and BD2 were

readily obtained in the 12 500–22 000 cm−1 region as shown in

Fig. 2. Our spectrum of BH2 extends some 5500 cm−1 to higher

wavenumbers of that reported by Herzberg and Johns,15 and

the present spectra of BD2 are new information. In each case,

the major progression of bands is readily identified, based on

the calculated band positions given by Kolbuszewski et al.,19

modified as necessary by our own calculations (see Sec. IV),

as the bending progression, and extending from v′2= 10 to 19

in 11BH2 and v′2= 14 to 23 in 11BD2. As primarily K ′′a = 0

and 1 BH2 levels are populated in our supersonic expansion

(in some cases we also see weaker transitions from K ′′a = 2),

the ΔKa = ±1 selection rule necessitates that the transitions

terminate on K ′a = 1 or Π levels for v′2= even and K ′a = 0

or 2 (Σ or Δ) levels for v′2= odd, leading to the Π, Σ band

alternation observed in the spectrum and proven by rotational

analysis (vide infra). The BH2–BD2 vibronic band isotope

effects are very large (∼3300 cm−1 for the transitions to

the v′2= 14 Π bands—see Fig. 2). In most cases, weaker

10B isotopologue bands were identifiable 50-150 cm−1 to

higher wavenumbers of the stronger features as illustrated in

Fig. 3. In addition, other weaker bands were vibronically as-

signed as transitions to excited state bend-stretch combination

levels and to mixed ground/excited state levels based on the

results of our theoretical calculations (see Secs. IV and V).

FIG. 2. Composite medium resolution

LIF spectra of BH2 and BD2. These

spectra were constructed by piecing to-

gether multiple scans over several laser

dye regions so the relative intensities of

the various bands are not very meaning-

ful. The major bending progression 2n0

is identified in each case.



FIG. 3. Two medium resolution bands

showing the 11B–10B isotope shifts in

the spectra of BH2 and BD2. In each

case, the central Q-branch of the par-

ticular isotopologue is identified.

As an example of the rotational analysis of the bands,

we show in Fig. 4 the LIF spectrum of the 2100

band of11BH2, illustrating the well-resolved rotational structure at

modest resolution (0.1 cm−1) and some of the rotational

assignments. The 2100

band involves the transition from

K ′′ = 0 to K ′ = 1 and is therefore a Π type band and clearly

exhibits the expected intensity alternation due to the lower

state nuclear statistical weights. Although the corresponding

K ′′ = 2 to K ′ = 1 subband might also be expected at lower

wavenumbers, no trace of it was found, due to the weakness

of the main subband and the effective cooling in the supersonic

expansion. [These weaker subbands were found in some

cases for the stronger vibronic transitions and they are very

useful for making further ground state combination differences

(GSCDs).] The rR0 branch lines are readily apparent at the blue

end of the band and were assigned based on the regular pattern

of transitions and intensity alternations. The rP0 lines were

then readily located using rR0(N ′′) − rP0(N ′′ + 2) GSCDs

[both sets of lines terminate on the same N ′KaKc level in the

upper state] in comparison to those derived from Table III of

Ref. 15. Since the Q-branch lines terminate on the opposite

asymmetry component in the excited state [for example, rR0(1)is 211-101 (NKaKc), whereas rQ0(2) is 212-202], it was not

FIG. 4. The medium-resolution sync-scan LIF spectrum of the 2100Π band of

11BH2. The vertical leaders identify the rotational branches and assignments.

possible to form GSCDs with the P- or R-branch lines, so

assignments were made based largely on intensities and the

expected pattern of lines. No spin splittings are evident in any

of the lines in this particular band at this resolution.

For examples of Σ and Δ bands, we show in Fig. 5 the 2150

spectrum of 11BD2. The Σ band involves a K ′ = 0 − K ′′ = 1

transition, while the Δ band originates in the same lower

state K stack but terminates in the K = 2 (Δ) component of

the A(0,15,0) vibrational state. The most obvious features

of the Σ band are the well-resolved pR1 branch and the

corresponding very compact Q-branch. Comparison of the

R-branch lines of a Σ band and a Π band (Fig. 4) shows

two diagnostic differences. In the Σ band, the separation of

the first lines of the R- and Q-branches is large, approximately

4B′ [for 11BD2 (0,15,0), this is ∼12 cm−1], as the two terminate

on the N ′ = 1 and N ′ = 2 levels. In a Π band of 11BD2

(not shown), this separation is the difference between the

K ′′a = 0, N ′′ = 0 and N ′′ = 1 levels, approximately B′′ + C ′′,which for the (0,16,0) 11BD2Π band is ∼5.5 cm−1, about

half that of the neighboring Σ band. Second, in a given

isotopologue, the pattern of R-branch intensity alternation

is different. In BH2, the first Π band R-branch line is weak

(lower level = 00,0 or ee) and the first Σ band line is strong

(lower level = 11,0 or oe). The situation is exactly reversed in

BD2. The analysis of the Σ bands proceeded much the same

as that of the Π bands described above. Since the energy level

separations are known for the ground state, and there are no

asymmetry splittings in the K = 0 upper state, in this case, it

was possible to form ground state combination differences for

all three branches.

The upper state bending levels shown in Fig. 1 are the

simplest cases at very low values of v′2. For higher levels with

odd v′2, there is a manifold of Σ, Δ, Γ (K = 0,2,4, . . .), etc.,

levels, and for even v′2, there are Π, Φ, H (K = 1,3,5, . . .), etc.

levels. Since we observe that jet-cooling populates primarily

the K ′′a = 0 and 1 stacks of rotational levels, only transitions

to the upper state K = 0 (Σ), K = 1 (Π), and K = 2 (Δ)levels are expected. This means that only a single Π band

is expected for even v′2

but transitions to odd v′2

should

consist of closely spaced Σ and Δ subbands as is found for

(0,15,0) of 11BD2 and shown in Fig. 5. According to Pople and



FIG. 5. Medium resolution LIF spec-

tra of the 2150

band of 11BD2. The

leaders identify the branches of the Σ

band (darker shading, shaded blue on-

line). Some of the rotational lines of

the nearby Δ band at lower energies are

also identified (lighter shading, shaded

yellow online). The inset shows the four

spin- and asymmetry-split components

of the rR1(1) transition of the Δ band.

Longuet-Higgins,32 such upper state vibrational levels with

v2 > K can be represented by

G(v2,K) = ω2(v2 + 1) + x22(v2 + 1)2 − GK2, (1)

where G is a positive quantity depending on the potential

constants. This equation implies that the Δ subband should be

below the Σ, as is observed. The major difference between the

Σ and Δ bands is that the latter show characteristic asymmetry

splittings. For example, the rR1(1) transition must consist of

two lines, 22,1← 11,0 and 22,0← 11,1 with a consistent splitting

of ∼0.6 cm−1 (∼1.2 cm−1 for 11BH2). As is shown in the inset

to Fig. 5, this line actually consists of four components, as the

asymmetry components are further spin-split.

In their original work, Herzberg and Johns15 only found

spin doublings in the (0,9,0) Δ − Π band at 11 700 cm−1, with

an interval of about 0.3 cm−1. In our work, we were able to

identify spin splittings in several of the bands terminating on

Π or Δ states. It is clear from our calculations and those of

others18,19 that the spin multiplets in the lowest vibrational

level of the ground state are regular with the energy of the

J = N + 1/2(F1) component higher than that of J = N − 1/2(F2)for a given NKa,Kc and there is no appreciable spin splitting

for the K ′′a = 0 levels. In the excited state, the Σ (K = 0)

levels are also not spin-split but the higher K (Π, Δ, . . .)levels often have appreciable spin splittings, which may be

regular or inverted depending on the identity of the vibrational

state and whether or not it is perturbed. We have assigned

the J quantum numbers in our spectra based on the relative

intensities at the beginning of the branch, with the usual

expectation that ΔJ = ΔN transitions should be strongest, and

that transitions originating in the F1 levels should be more

intense than those from F2 due to the greater 2J + 1 degeneracy

of the former. For example, the (0,14,0)Π band shows spin

splittings in all the branches. The rR0(0) transition has two

lines at 16 383.80 cm−1 (intensity = 1.7) and 16 385.09 cm−1

(intensity = 1.0) with a splitting of 1.29 cm−1. The higher

intensity line is assigned as J = 1.5← J = 0.5 (ΔJ = ΔN)

and the weaker as J = 0.5← J = 0.5 so that the upper state

level is inverted with the energy of J = 0.5 > J = 1.5. The

next rR0(1) line has a spin splitting of 0.73 cm−1 with the

lower wavenumber line stronger than the higher wavenumber

feature. The lower state levels have J = 1.5 (2J + 1 = 4)and J = 0.5 (2J + 1 = 2) so the transitions are assigned as

J = 2.5← J = 1.5 (lower) and J = 1.5← J = 0.5 (upper),

again inverted. The fact that the rP0(2) and rP0(3) transitions

have the same measured spin-splittings as those of rR0(0)and rR0(1) proves that the lower state K = 0 levels are not

spin-split. In this fashion, J values were assigned to all the

spin-split transitions in our LIF spectra.

In the expected region of the (0,14,0) Π band of11BH2, we observed two Π bands, whose rR0(0) transitions

(see Table I) are separated by 91.5 cm−1 and have opposite

spin-splittings in the upper state such that the lower energy

band has inverted spin levels, whereas the higher is regular.

Initially, it proved difficult to make upper state vibronic assign-

ments of these two bands but once the ab initio calculations of

the spin-rovibronic levels were available (vide infra), the cause

of the anomaly was clear. The calculations show that there is a

strong, almost 50:50 mixing of the excited state (0,14,0) K = 1

rotational levels with the higher (0,13,0) Ka = 1 levels of the

ground state so that transitions to the latter gain intensity

and can be observed experimentally. The calculated upper

state energies agree with the measured transition frequencies

(see Table I) and the observed and calculated rR0(0)

spin splittings agree in sign and magnitude (A(0,14,0):obs = −1.3 cm−1, calc = −0.99 cm−1; X(0,13,0): obs

= +1.1 cm−1, calc = +1.03 cm−1). There can be little doubt

that the assignments are correct. In a similar fashion, we were

able to assign a pair of 11BD2 bands at 14 443 and 14 509 cm−1

as transitions to A(0,16,0) and X(0,16,0), respectively.

In summary, we have assigned 67 bands of the four

isotopologues of BH2. In addition, there are a variety

of weak band fragments, groups of lines, and even sin-

gle lines scattered throughout the spectra which have no

detailed assignments. In order to make comparisons with our

theoretical predictions, we report in Tables I and II the specific



TABLE I. A comparison of the experimentally measured transition frequencies (in cm−1) of the assigned LIF

bands of 11BH2 and 10BH2 and their theoretically predicted values.

11BH210BH2

Band Expt.a Theoryb Expt. Theoryc

(0,9,0)Σ 11 718.72* 11 717.9 11 779.72* 11 775.1

(0,9,0)Δ 11 717.18* 11 714.2 ... 11 776.3

(0,10,0)Π 12 703.48 12 701.7 ... 12 763.6

(0,11,0)Σ 13 591.94 13 591.5 13 660.08 13 658.7

(0,11,0)Δ 13 569.62 13 568.8 ... 13 632.3

(0,12,0)Π 14 570.80 14 569.9 14 641.36 14 638.7

(1,10,0)Π 15 217.97d 15 218.5 ... 15 292.9

(0,13,0)Σ 15 457.34 15 457.0 15 530.87 15 533.0

(0,13,0)Δ 15 414.28/15.19 15 416.3 ... 15 495.1

(1,11,0)Σ 16 102.77 16 103.8 ... 16 176.3

(0,14,0)Π 16 383.80/85.09 16 386.9 ... 16 480.3

X(0,13,0)e 164 75.43/76.53 16 475.7 16 571.69d 16 571.0

(1,12,0)Π 17 065.61 17 070.7 ... 17 149.7

(0,15,0)Σ 17 314.49 17 314.6 17 398.75 17 398.7

(0,15,0)Δ 17 337.03/37.79 17 335.7 17 426.24/27.09 17 424.9

(1,13,0)Σ 17 949.23 17 951.0 ... 18 032.8

(0,16,0)Π 18 294.74/95.06 18 292.5 18 385.00 18 385.5

(1,14,0)Π 18 927.16/27.56 18 926.1 ... 19 014.6

(0,17,0)Σ 19 163.63 19 163.9 19 255.27 19 255.5

(0,17,0)Δ 19 163.03 19 163.2 19 256.12 19 256.0

(0,18,0)Π 20 134.76 20 134.3 20 231.69 20 231.0

(0,19,0)Σ 21 003.69 21 004.9 ... 21 103.2

(0,19,0)Δ 20 997.10 20 999.6 ... 21 099.2

aFor Σ bands this is pP1(1), for Π bands rR0(0), and for Δ bands= rR1(1). Both values are reported for spin-split transitions.

All measurements ±0.1 cm−1. Experimental values with * from Ref. 15.bFor Σ and Δ states, 48.5 cm−1 (average of the two spin components of the ground state 110 level) has been subtracted.cFor Σ and Δ states, 49.1 cm−1 (average of the two spin components of the ground state 110 level) has been subtracted.dTentative assignment, overlapped or otherwise complicated.eTransition to ground state level.

rovibronic transition in each band that is from the lowest

accessible ground state rotational level to the lowest energy

accessible upper state rotational level. For Σ bands, this

is A(000) − X(110) = pP1(1), for Π bands = A(110) − X(000)= rR0(0), and Δ bands = A(220) − X(110) = rR1(1). If the line

is spin-split, then the frequencies of both spin-components are

reported. We have elected not to fit the rotational lines of each

band to any particular energy level formula as preliminary

studies showed that most of the bands were perturbed in some

fashion, making the constants unreliable. Instead, the detailed

line assignments for all the bands we have analyzed have been

given in the supplementary material.33

C. High resolution LIF spectra

In previous work, the ground state rotational constants of11BD2 were necessarily very imprecise,15 which hindered the

determination of an accurate molecular structure. In an effort

to rectify this deficiency, we recorded high resolution spectra

of the Π − Σ (K = 1 − Ka = 0) and Π − Δ (K = 1 − Ka = 2)

subbands of the 2200

band of 11BD2. Portions of these spectra

are shown in Fig. 6 along with the assignments. The K ′= 1 − K ′′a = 0 subband is quite strong, and the P-, Q-, and R-

branches are readily identified, including the very small spin-

splittings at low N . In contrast, the K ′ = 1 − K ′′a = 2 subband

is very weak, primarily due to the efficient cooling which

depopulates the K ′′a = 2 levels, but the branches, which include

asymmetry and spin-splittings, were reliably identified using

GSCDs. We then fitted the GSCDs to obtain a set of v′′ = 0

rotational constants for 11BD2 which are given along with the

previous 11BH2 constants15 in Table III. The individual line

measurements and assignments are given in Table IV.

IV. THEORETICAL CALCULATIONS

A. Calculation of the potential energy surfaces

The Potential Energy Surfaces (PESs) for the bent ground

X2A1 and the linear A2B1 first excited states of BH2 were

constructed from the fit of a large number of single point

energy calculations. The geometries of the single point

calculations were carefully chosen in order to properly map

both PESs for energies up to 22 000 cm−1 above the minimum

of the X2A1 state. In summary, 777 points were calculated

for the X2A1 state and 461 points for the A2B1 state. The

geometries were in the ranges 1.6 ≤ rBH1 ≤ 3.7 bohrs, with

rBH2 ≥ rBH1, for the stretching coordinates (all states) and

60 ≤ θHBH ≤ 180 (X2A1) or 90 ≤ θHBH ≤ 180 (A2B1). The

total energy E at each geometry was obtained in a stepwise

manner, such that

E = EV5Z + ΔECC + ΔECBS + ΔEFCI + ΔEBO, (2)



TABLE II. A comparison of the experimentally measured transition frequencies (in cm−1) of the assigned LIF

bands of 11BD2 and 10BD2 and their theoretically predicted values.

11BD210BD2

Band Expt.a Theoryb Expt.a Theoryc

(0,14,0)Π 13 073.69/74.00 13 069.3 ... 13 172.4

(1,12,0)Π 13 529.58/29.87 13 526.4 ... 13 631.7

(0,15,0)Σ 13 744.90 13 741.2 13 851.77 13 847.8

(0,15,0)Δ 13 727.11/27.43 13 725.1 ... 13 840.4

(1,13,0)Σ 14 197.11 14 194.0 14 299.96 14 298.3

(1,13,0)Δ 14 180.84/81.05 14 180.2 ... 14 287.6

(0,16,0)Π 14 443.14/44.30 14 441.7 14 564.97/65.83 14 562.1

X(0,16,0)d 14 508.68/09.81 14 506.6 ... 14 653.9

(0,17,0)Σ 15 130.00 15 126.3 15 245.95 15 242.4

(0,17,0)Δ 15 144.21/44.98 15 140.9 ... 15 266.1

(1,15,0)Σ 15 583.88 15 581.0 ... 15 695.9

(0,18,0)Π 15 849.23 15 846.2 15 971.43 15 967.4

(1,16,0)Π 16 307.75/08.25 16 305.7 ... 16 433.3

(0,19,0)Σ 16 507.57 16 504.1 16 632.32e 16 629.0

(0,19,0)Δ 16 505.66 16 502.3 16 632.32e 16 628.9

(1,17,0)Σ 16 962.52 16 959.9 ... 17 084.6

(1,17,0)Δ 16 959.17 16 955.8 ... 17 085.6

(0,20,0)Π 17 220.61 17 216.9 17 351.25 17 347.3

(1,18,0)Π 17 662.91/63.35 17 663.1 ... 17 800.9

(0,21,0)Σ 17 877.95e 17 874.5 18 011.20 18 007.6

(0,21,0)Δ 17 871.32 17 868.9 ... 18 004.7

(1,19,0)Σ 18 332.75 18 330.8 ... 18 464.8

(1,19,0)Δ 18 330.84 18 328.6 ... 18 467.6

(0,22,0)Π 18 585.52/85.87 18 582.5 18 723.86/24.16 18 720.6

(1,20,0)Π 19 057.50 19 040.9 ... 19 178.8

(0,23,0)Σ 19 241.41 19 237.9 ... 19 378.6

aFor Σ bands this is pP1(1), for Π bands rR0(0), and for Δ bands= rR1(1). Both values are reported for spin-split transitions.

All measurements ±0.1 cm−1.bFor Σ and Δ states, 27.3 cm−1 (average of the two spin components of the ground state 110 level) has been subtracted.cFor Σ and Δ states, 27.8 cm−1 (average of the two spin components of the ground state 110 level) has been subtracted.dTransition to ground state level.eTentative assignment, overlapped or otherwise complicated.

where EV5Z is the energy calculated at the coupled cluster

singles and doubles with perturbative triples [CCSD(T)]level

of theory35 with the aug-cc-pV5Z basis,34 ΔECC is a correction

for the correlation effects of core electrons, ΔECBS is an

estimate of the complete basis set limit within the frozen core

approximation, ΔEFCI is an estimate of electron correlation

beyond CCSD(T), andΔEBO takes into account diagonal Born-

Oppenheimer corrections.

The ΔECC correction was determined by taking the

difference between energies at the CCSD(T) level, calculated

either with all electrons correlated and the aug-cc-pwCV5Z

basis36 or with valence electrons only and the aug-cc-pV5Z

FIG. 6. High resolution LIF spectra of

the two Π subbands of the 2200

transi-

tion of 11BD2. The upper trace shows

the Ka = 1−2 subband which exhibits

resolved spin- and asymmetry-splittings

in the various branches. The lower trace

is the much stronger Ka = 1−0 sub-

band which shows partially resolved

spin-splittings at low N .



TABLE III. The effective ground state rotational constants of BH2 and BD2.

All values reported in this table are in cm−1.

Rotational constant 11BH211BD2

A0 41.649(8)a 23.321(1)

B0 7.241(1) 3.627(2)

C0 6.001(2) 3.094(2)

aBH2 values from Ref. 15, BD2 from this work. The corresponding theoretical rotational

constants are: A0= 42.0541 cm−1, B0= 7.2330 cm−1, C0= 6.0175 cm−1 for 11BH2,

and A0= 23.7301 cm−1, B0= 3.6287 cm−1, C0= 3.0931 cm−1, for 11BD2. These in

turn have been evaluated from the theoretical equilibrium geometry (see Table VII) by

applying second order perturbation theory to the analytical PESs.

basis. The ΔECBS correction was obtained from the energies

calculated at the CCSD(T) level with the aug-cc-pVQZ and

aug-cc-pV5Z basis sets,34 by performing an extrapolation

towards the complete basis set limit using the procedure

outlined by of the Schwenke.37

For the ΔEFCI term, a full CI computation38 was per-

formed with the cc-pVTZ basis, and the difference between

full CI and CCSD(T) energies, with the same basis, was

taken. For computational reasons, only valence electrons were

correlated and only geometries which can be handled in C2v

symmetry by the quantum chemistry package were considered.

These include all linear geometries and a subset of bent

geometries, those with both rBH bond lengths kept fixed at

2.2 bohrs. The ΔEFCI correction at any geometry was then

approximated as

ΔEFCI(r1,r2, θ) = ΔEFCI(r1,r2,180◦) + [ΔEFCI(2.2,2.2, θ)− ΔEFCI(2.2,2.2,180◦)] , (3)

where r1, r2 correspond to the rBH1 and rBH2 bond lengths and

θ is the θHBH angle.

The last ΔEBO term accounts for isotope-dependent

diagonal Born-Oppenheimer corrections39 to the adiabatic

surfaces. It was evaluated by calculating the geometry

dependence, at the CASSCF/aug-cc-pwCV5Z level, of the

L2x, L

2y, L

2z, and Lx Lz angular momentum operator matrix

elements, as exploited in Eq. (1b) of Ref. 40. Their values

are usually taken as zero for the L2x, L

2y, and Lx Lz operators

and one for L2z operator, for all geometries. The influence of

the inclusion of the geometry dependence of these operators

has been discussed in detail in Ref. 41. TheΔEBO term depends

on the masses of the atoms and it has been computed from the

following equation:40,42

ΔEkBO(r1,r2, θ) = 1

8 cos2(θ/2)(

1

μ1r12+

1

μ2r22+

2

mr1r2

)

× ��k |L2

z |k� − 1

�

+1

8 sin2(θ/2)(

1

μ1r12+

1

μ2r22− 2

mr1r2

)

× �k |L2

x |k�

+1

8

(1

μ1r12+

1

μ2r22+

2 cos θ

mr1r2

) ⟨k |L2

y |k⟩

− 1

4 sin θ

(1

μ1r12− 1

μ2r22

)

× �k |Lx Lz + Lz Lx |k� , k = X2A1, A2B1,

(4)

where r1, r2 correspond to the rBH1 and rBH2 bond lengths, θ is

the θHBH angle, m is the mass of the central B atom, and μ1 and

μ2 are the reduced masses between the central B atom and the

peripheral H1 and H2 atoms (see Ref. 40 for further details).

All the CCSD(T) calculations needed to set up Eq. (2)

were performed with the CFOUR suite of quantum chemistry

programs.43 Full CI energies and angular momentum matrix

elements were obtained with the Molpro 2010 code.44

The discrete energies of the two states, as defined by

Eq. (2), were fitted using the SURFIT program,45 using

symmetry restricted polynomial functions with the general

form

Vη(r1,r2, θ) =∑ijk

cηijk(q1 − qref ,η1)i(q2 − qref ,η2

) j(q3 − qref ,η3)k,

(5)

where η refers to a specific electronic state and isotopologue,

q1 = (r1 + r2)/√

2 (symmetric stretch), q2 = (r1 − r2)/√

2 (anti-

symmetric stretch), and q3 = θHBH; qref ,η1

, qref ,η2

, and qref ,η3

define the reference geometry of the η-th state. Symmetry

restrictions constrain j to be even for both states and kto be even for the A2B1 state. The two PESs of four

different isotopologues (11BH2,10BH2,

11BD2,10DB2) have

been obtained in this way and the corresponding fitting

coefficients cηijk are reported with and without the mass-

dependent corrections as supplementary material.33 The root

mean square deviations (RMSDs) of the fittings were 4.1 cm−1

for the lower (X2A1, ground state) surface and 0.6 cm−1 for the

upper (A2B1 excited state) surface. The degeneracy of the two

surfaces at linearity was imposed by simply including 52 linear

geometries (1.7 ≤ rBH1 ≤ 2.8 bohrs, rBH2 ≥ rBH1) in the fitting

of the ground state coefficients. This procedure was much

simpler than that adopted previously for HBF,11 and it was able

to recover surfaces which are nearly degenerative for linear

geometries, with differences of the same order of magnitude

of the RMSDs of the fittings. These tiny differences proved to

be irrelevant in the subsequent variational calculation of the

rovibronic energy levels.

The Molpro code was also used to calculate the phenome-

nological spin-orbit splitting of the electronicΠ (X2A1, A2B1)

state. At the computed equilibrium geometry of the A2B1 state,

using the CASSCF level of theory and the aug-cc-pV5Z basis,

the splitting was 7.72 cm−1, which is in a very good agreement

with the empirical value of 7.93 cm−1 found by Kolbuszewski

et al.19 This was taken as a geometry independent parameter

and used in all subsequent variational calculations.

B. Calculation of the rovibronic energy levels

The ab initio surfaces were used for the variational

calculation of the rovibronic energy levels. Preliminary

analyses were performed using the RVIB3 code developed

by Carter and co-workers.46 However, in the course of these

tests, a paper by Mitrushchenkov was published,47 pointing

out some numerical difficulties in the RVIB3 code and its

underlying theory in the handling of cases with very large

Renner-Teller coupling, such as linear-bent systems. These

difficulties become evident only in the calculation of levels

with Ka > 0 (Π, Δ, etc., states). We then resorted to using a



TABLE IV. The individual transition measurements and assignments from the high-resolution LIF spectrum of

the 2200

band of 11BD2.

Branch N ′, Ka′, Kc

′, J ′ N ′′, Ka′′, Kc

′′, J ′′ Line position

K′= 1←Ka′′= 0 rR0(0) 1, 1, 0, 1.5 0, 0, 0, 0.5 17 220.597

rR0(0) 1, 1, 0, 0.5 0, 0, 0, 0.5 17 220.743rR0(1) 2, 1, 1, 2.5 1, 0, 1, 1.5 17 227.164?rR0(1) 2, 1, 1, 1.5 1, 0, 1, 0.5 17 227.229?rR0(2) 3, 1, 2, 3.5 2, 0, 2, 2.5 17 233.783rR0(2) 3, 1, 2, 2.5 2, 0, 2, 1.5 17 233.836rR0(3) 4, 1, 3a 3, 0, 3 17 240.458rR0(4) 5, 1, 4 4, 0, 4 17 247.255rQ0(1) 1, 1, 1, 1.5 1, 0, 1, 1.5 17 213.138rQ0(1) 1, 1, 1, 0.5 1, 0, 1, 0.5 17 213.276rQ0(2) 2, 1, 2, 2.5 2, 0, 2, 2.5 17 211.528rQ0(2) 2, 1, 2, 1.5 2, 0, 2, 1.5 17 211.591rQ0(3) 3, 1, 3, 3.5 3, 0, 3, 3.5 17 209.168rQ0(3) 3, 1, 3, 2.5 3, 0, 3, 2.5 17 209.186rQ0(4) 4, 1, 4 4, 0, 4 17 206.155rQ0(5) 5, 1, 5 5, 0, 5 17 206.616rQ0(6) 6, 1, 6 6, 0, 6 17 198.787rP0(2) 1, 1, 0, 1.5 2, 0, 2, 2.5 17 200.447rP0(2) 1, 1, 0, 0.5 2, 0, 2, 1.5 17 200.591rP0(3) 2, 1, 1, 2.5 3, 0, 3, 3.5 17 193.693?rP0(3) 2, 1, 1, 1.5 3, 0, 3, 2.5 17 193.704?rP0(4) 3, 1, 2, 3.5 4, 0, 4, 4.5 17 186.926rP0(4) 3, 1, 2, 2.5 4, 0, 4, 3.5 17 186.968rP0(5) 4, 1, 3 5, 0, 5 17 180.367rP0(6) 5, 1, 4 6, 0, 6 17 174.027

K′= 1←Ka′′= 2 pR2(2) 3, 1, 3, 3.5 2, 2, 1, 2.5 17 149.311

pR2(2) 3, 1, 3, 2.5 2, 2, 1, 1.5 17 149.503pR2(2) 3, 1, 2, 3.5 2, 2, 0, 2.5 17 153.819pR2(2) 3, 1, 2, 2.5 2, 2, 0, 1.5 17 154.030pR2(3) 4, 1, 4, 4.5 3, 2, 2, 3.5 17 152.871pR2(3) 4, 1, 4, 3.5 3, 2, 2, 2.5 17 153.002pR2(3) 4, 1, 3, 4.5 3, 2, 1, 3.5 17 160.358pR2(3) 4, 1, 3, 3.5 3, 2, 1, 2.5 17 160.507pR2(4) 5, 1, 5, 5.5 4, 2, 3, 4.5 17 155.776pR2(4) 5, 1, 5, 4.5 4, 2, 3, 3.5 17 155.879pR2(4) 5, 1, 4, 5.5 4, 2, 2, 4.5 17 166.898pR2(4) 5, 1, 4, 4.5 4, 2, 2, 3.5 17 167.022pR2(5) 6, 1, 6, 6.5 5, 2, 4, 5.5 17 158.249pR2(5) 6, 1, 6, 5.5 5, 2, 4, 4.5 17 158.313pQ2(2) 2, 1, 2, 2.5 2, 2, 0, 2.5 17 131.563pQ2(2) 2, 1, 2, 1.5 2, 2, 0, 1.5 17 131.784pQ2(3) 3, 1, 2, 3.5 3, 2, 2, 3.5 17 133.652pQ2(3) 3, 1, 2, 2.5 3, 2, 2, 2.5 17 133.820pQ2(3) 3, 1, 3, 3.5 3, 2, 1, 3.5 17 129.092pQ2(3) 3, 1, 3, 2.5 3, 2, 1, 2.5 17 129.226pQ2(4) 4, 1, 4, 4.5 4, 2, 2, 4.5 17 125.809pQ2(4) 4, 1, 4, 3.5 4, 2, 2, 3.5 17 125.914pQ2(5) 5, 1, 5, 5.5 5, 2, 3, 5.5 17 121.818pQ2(5) 5, 1, 5, 4.5 5, 2, 3, 4.5 17 121.895pQ2(5) 5, 1, 4, 5.5 5, 2, 4, 5.5 17 133.478pQ2(5) 5, 1, 4, 4.5 5, 2, 4, 4.5 OLb

pP2(2) 1, 1, 0, 1.5 2, 2, 0, 2.5 17 120.480pP2(2) 1, 1, 0, 0.5 2, 2, 0, 1.5 17 120.785pP2(2) 1, 1, 1, 1.5 2, 2, 1, 2.5 17 119.752pP2(2) 1, 1, 1, 0.5 2, 2, 1, 1.5 17 120.035pP2(3) 2, 1, 1, 2.5 3, 2, 1, 3.5 17 113.554pP2(3) 2, 1, 1, 1.5 3, 2, 1, 2.5 17 113.732pP2(3) 2, 1, 2, 2.5 3, 2, 2, 3.5 17 111.400pP2(3) 2, 1, 2, 1.5 3, 2, 2, 2.5 17 111.572



TABLE IV. (Continued.)

Branch N ′, Ka′, Kc

′, J ′ N ′′, Ka′′, Kc

′′, J ′′ Line position

pP2(4) 3, 1, 2, 3.5 4, 2, 2, 4.5 17 106.592pP2(4) 3, 1, 2, 2.5 4, 2, 2, 3.5 17 106.740pP2(4) 3, 1, 3, 3.5 4, 2, 3, 4.5 17 102.247pP2(4) 3, 1, 3, 2.5 4, 2, 3, 3.5 17 102.364pP2(5) 4, 1, 3, 4.5 5, 2, 3, 5.5 17 099.543pP2(5) 4, 1, 3, 3.5 5, 2, 3, 4.5 17 099.649pP2(5) 4, 1, 4, 4.5 5, 2, 4, 5.5 17 092.374(OL)pP2(5) 4, 1, 4, 3.5 5, 2, 4, 4.5 17 092.461(OL)

aThe J quantum number is omitted from transitions that did not exhibit resolved splittings. Transitions with a question mark are

perturbed or otherwise irregular.bOL= overlapped.

previous version of the code, based on a different definition

of the basis set for the bending motion,40 which has proved to

work correctly for linear-bent systems.18,41

The variational basis set of the two electronic states was

built from 20 harmonic oscillators for the stretches and 104

Legendre polynomials for the bend, contracted to 25 two-

dimensional stretching functions and 61 two dimensional

bending functions.

Spin-rovibronic calculations for J = 1/2, 3/2, 5/2, and 7/2

were performed, thus enabling the prediction of the energies

for all rovibrational levels with Ka ≤ 3 (Σ,Π,Δ,Φ levels). The

vibrational quantum numbers were assigned by inspection of

the variational coefficients and, for higher levels, by counting

the nodes in plots of the vibrational wavefunctions. All four

experimentally relevant isotopologues (11BH2,10BH2,

11BD2,10BD2) were studied, for energies up to 22 000 cm−1 above the

X2A1(000) level.

The comparison between the observed and calculated

transition frequencies for the various observed bands of BH2

and BD2 is presented in Tables I and II. The agreement between

the two quantities is excellent, with differences of only a

few cm−1 in each case. We show in Tables V and VI, the

lowest calculated vibrational levels of the ground state and

the calculated pure bending levels of the excited state up to

22 000 cm−1, respectively. The relevant results of the present

TABLE V. Calculated low-lying X2A1 state vibrational energy levels

(NKa,Kc = 000) of the various BH2 isotopologues (in cm−1).

(v1,v2,v3) 11BH211BD2

10BH210BD2

(0,1,0) 972.9 733.0 979.1 740.5

(0,2,0) 1910.9 1435.6 1923.4 1450.1

(1,0,0) 2508.1 1818.4 2511.6 1823.6

(0,0,1) 2658.4 2017.3 2674.8 2039.5

(0,3,0) 2857.4 2114.0 2877.5 2135.9

(1,1,0) 3482.1 2552.8 3492.0 2565.9

(0,1,1) 3630.9 2750.9 3653.5 2780.6

(0,4,0) 3866.2 2795.7 3894.7 2826.5

(1,2,0) 4421.9 3256.3 4438.5 3276.6

(0,2,1) 4566.8 3455.8 4595.5 3492.4

(0,5,0) 4951.1 3514.2 4988.0 3555.1

(2,0,0) 4964.6 3612.4 4971.7 3622.8

(1,0,1) 5078.4 3790.2 5097.9 3817.4

(0,0,2) 5270.1 4003.7 5301.4 4046.9

ab initio computations compared to previous studies18,19 are

summarized in Table VII.

V. DISCUSSION

A. Molecular structure

The determination of the ground state rotational constants

of two different isotopomers of 11BH2 allows a precise

evaluation of the effective zero-point molecular structure.

Planar moments (PA,B, or C), rather than the raw rotational

constants or moments of inertia, were used for the least squares

analysis to minimize correlations between the geometric

parameters. Since the out-of-plane planar moment PC must

by definition be zero, the data set included only PA and PB of11BH2 and 11BD2. Allowance was made for a slight decrease

(0.003 Å) in the B–H bond length upon deuteration. The

resulting structure is

r0(BH) = 1.197(2) Å, θ0 = 129.6(2)◦,where the numbers in parentheses are one standard error. The

agreement between the experimental and ab initio values of

r0(BH) = 1.195 Å and θ0 = 129.9◦ is excellent. (The ab initiovalues have been obtained by applying the same analysis to

the theoretical rotational constants as reported in the footnote

to Table III.) The BH bond length is 0.017 Å shorter than

that of the HBF free radical48 and is ∼0.035 Å shorter than

the equilibrium ground state bond length (1.2322 Å) of the

BH radical.49 The short BH bond length is entirely consistent

with a BH2 symmetric stretching frequency of 2508 cm−1

(Table VII) which is substantially larger than the ω01= 2433

and ωe = 2366.7 cm−1 BH stretching frequencies of HBF and

BH, respectively. The BH2 bond length is almost identical to

the r0 = 1.190 Å bond length of gas phase BH3.50

B. Comparison between theory and experiment

In contrast to previous theoretical studies,18,19 no attempts

were made to improve our ab initio surfaces empirically.

Nevertheless, the accuracy of the calculated vibronic levels

is similar to that routinely obtainable in pure vibrational spec-

troscopy applications, i.e., better than 5 cm−1. To our knowl-

edge, such accuracy has never before been reached in compu-

tational spectroscopy studies of Renner-Teller molecules.



TABLE VI. Calculated A2B1 state vibronic (N =Ka) bending levels, rela-

tive to the lowest rovibrational level of the electronic ground state, of the BH2

isotopologues (in cm−1). For Π, Δ, and Φ states, the average of Kc and spin

components is reported.

(v1,v2,v3) 11BH211BD2

10BH210BD2

(0,1,0)Σ 4 191.6 3 834.7 4 203.2 3 850.0

(0,2,0)Π 5 076.3 4 489.0 5 096.4 4 517.7

(0,3,0)Δ 5 850.1 5 019.3 5 879.3 5 064.9

(0,3,0)Σ 6 097.6 5 283.1 6 122.5 5 315.3

(0,4,0)Φ 6 602.6 5 826.8 6 641.6 5 875.9

(0,4,0)Π 7 061.6 5 985.1 7 098.5 6 027.7

(0,5,0)Δ 7 924.2 6 623.9 7 964.6 6 675.1

(0,5,0)Σ 7 995.4 6 720.4 8 032.3 6 768.0

(0,6,0)Φ 8 761.3 7 179.9 8 808.0 7 250.1

(0,6,0)Π 8 917.6 7 373.0 8 961.4 7 437.2

(0,7,0)Δ 9 789.5 8 140.1 9 839.6 8 212.9

(0,7,0)Σ 9 884.9 8 147.7 9 933.0 8 209.2

(0,8,0)Φ 10 664.1 8 781.4 10 718.2 8 857.1

(0,8,0)Π 10 854.9 8 849.4 10 913.0 8 918.9

(0,9,0)Δ 11 762.7 9 514.7 11 825.4 9 593.8

(0,9,0)Σ 11 766.4 9 565.7 11 824.8 9 640.0

(0,10,0)Φ 12 654.4 10 151.8 12 720.6 10 238.9

(0,10,0)Π 12 701.7 10 265.9 12 763.6 10 345.4

(0,11,0)Δ 13 617.2 10 900.6 13 681.4 10 995.8

(0,11,0)Σ 13 639.9 10 974.8 13 707.8 11 060.9

(0,12,0)Φ 14 494.8 11 659.4 14 570.3 11 761.0

(0,12,0)Π 14 569.9 11 676.1 14 638.7 11 768.8

(0,13,0)Δ 15 464.7 12 358.5 15 544.2 12 458.7

(0,13,0)Σ 15 505.4 12 375.6 15 582.1 12 472.6

(0,14,0)Φ 16 308.3 13 027.9 16 397.8 13 130.5

(0,14,0)Π 16 386.9 13 069.3 16 480.3 13 172.4

(0,15,0)Δ 17 384.1 13 752.4 17 474.0 13 868.2

(0,15,0)Σ 17 363.0 13 768.5 17 447.8 13 875.6

(0,16,0)Φ 18 292.3 14 390.2 18 402.6 14 512.6

(0,16,0)Π 18 292.5 14 441.7 18 385.5 14 562.1

(0,17,0)Δ 19 211.6 15 168.2 19 305.1 15 293.9

(0,17,0)Σ 19 212.4 15 153.6 19 304.6 15 270.2

(0,18,0)Φ 20 114.0 15 843.7 20 214.2 15 970.6

(0,18,0)Π 20 134.3 15 846.2 20 231.0 15 967.4

(0,19,0)Δ 21 048.0 16 529.6 21 148.3 16 656.7

(0,19,0)Σ 21 053.3 16 531.4 21 152.3 16 656.8

(0,20,0)Φ 21 944.1 17 199.7 22 050.4 17 334.5

(0,20,0)Π 21 970.8 17 216.9 22 073.3 17 347.3

(0,21,0)Δ 17 896.2 18 032.5

(0,21,0)Σ 17 901.8 18 035.4

(0,22,0)Φ 18 556.8 18 699.3

(0,22,0)Π 18 582.4 18 720.6

(0,23,0)Δ 19 230.5 19 382.4

(0,23,0)Σ 19 265.1 19 406.4

(0,24,0)Φ 19 878.9 20 043.7

(0,24,0)Π 19 950.7 20 099.2

(0,25,0)Δ 20 633.7 20 780.0

(0,25,0)Σ 20 621.4 20 761.9

It is shown in Fig. 7 that all the corrections quoted in

Eq. (2) are important to achieve such an ambitious result.

The figure was constructed using the vibronic levels obtained

from preliminary PESs which included only part of the

corrections. All the remaining parameters of the Renner-Teller

code were kept fixed and the comparison was restricted to the

experimentally determined levels of 11BH2 reported in Table I.

When the PESs were constructed from points calculated

with just the EV5Z energies, a gross overestimation (RMSD

= 45.8 cm−1) of the vibronic levels is observed. However,

a significant improvement (RMSD = 29.9 cm−1) is obtained

by including the contribution of core correlation energy

(ΔECC), while the extrapolation to the complete basis set

limit (ΔECBS) is much less important, since it improves the

energies of most levels by only few wavenumbers (RMSD

= 28.2 cm−1). The effect of valence electron correlation

beyond CCSD(T), ΔEFCI, is comparable to that of core

correlation and is mandatory to reach reasonable spectroscopic

accuracy (RMSD = 4.5 cm−1). Unfortunately, the calculation

of this contribution is particularly time consuming, so only a

limited set of geometries in C2v was considered, extrapolating

the results to the whole surfaces, using Eq. (3). The inclusion of

the mass dependent correction (ΔEBO) is of minor importance

but it brings the predicted levels even closer to experiment

(RMSD = 2.1 cm−1).

The relevant properties of our PESs are summarized in

Table VII, where they are also compared to those reported

in Refs. 18 and 19. Both the topological and spectroscopic

results are very similar to previous results, with our values

slightly closer to those of Kolbuszewski et al.19 However,

the overall good accuracy of previous computations is partly

due to empirical corrections applied to the ab initio PESs,

in order to best reproduce the spectroscopic information

available at that time. In particular, the barrier to linearity

of the X2A1 state (i.e., the minimum of the A2B1 state) was

lowered by ∼100 cm−1 in both papers. The practice of making

moderate and intelligent adjustments to high level ab initiocomputations is very common, even in the recent literature

(see, e.g., Ref. 51 for recent application to the water molecule).

This is mainly due to the intrinsic limitations of the computer

technology rather than defects of the underlying theories.

Usually, these approaches are justified “ex post facto” by the

good predictive capabilities of the final models. However, care

must be taken when the set of data to which the calculations

are “tuned” is limited, either in number or in accuracy, since

“local” improvements may be achieved at the expense of a

global deterioration. In these cases, plain ab initio compu-

tations, even with limited accuracy, may prove to be more

reliable.

In the present work, we aimed to reach the highest

possible accuracy using only ab inito methods. With current

technology, this is possible only combining complementary

methods in conjunction with basis sets of different sizes. The

overall quality of such a hybrid yet fully ab initio approach is

clearly depicted by the graph at the bottom of Fig. 7 and by

the value of the barrier to linearity reported in Table VII.

Another important aspect of the synergy between theory

and experiment in this work was the identification of new,

unexpected bands in the LIF spectra of BH2 and BD2. In

particular, a Π band at 11BH2 at 16 475 cm−1 and the

corresponding band of 10BH2 at 16 572 cm−1 were assigned as

transitions to the ground state X(0,13,0) Ka = 1 levels which

are heavily mixed with the rotational levels of the (0,14,0) Π

vibronic excited state. Similarly, a fragment of a 11BD2 band at

14 509 cm−1 was identified from the calculations as a transition

to the ground state (0,16,0) Ka = 1 level which perturbs the



TABLE VII. Summary of relevant theoretical data for 11BH2.

X2A1 A2B1 (Πu)

Equilibrium geometry

Fundamental

frequencies/cm−1

Barrier to

linearity/cm−1

Equilibrium

geometry

T0/cm−1

Fundamental

frequencies/cm−1

rBH/Å θ/deg ν1 ν2 ν3 rBH/ Å ν1a ν2

b ν3c

Reference 18 1.184 128.68 2518 986 2667 2693d 1.167 4216 2597 950 2830

Reference 19 1.1875 129.04 2506.5 972.8 2657.9 2666e 1.1698 4203.9 2589.7 950.7 2825.1

This work 1.1844f 129.05f 2508.1 972.9 2658.4 2655.7g 1.1674f 4191.6 2592.1 953.0 2829.0

aThe difference A(1,1,0)Σ−A(0,1,0)Σ is reported.bThe value 1/2[A(0,3,0)Σ−A(0,1,0)Σ] is reported.cThe difference A(0,1,1)Σ−A(0,1,0)Σ is reported.dThis value is empirically corrected. The ab initio value is 2790 cm−1.eThis value is empirically corrected. The ab initio value is 2743 cm−1.f Minima of the analytical PESs without mass dependent corrections.gAb initio value obtained as difference between the energy minima of the analytical PESs without mass dependent corrections.

A(0,16,0) Π vibronic state. Such assignments would not have

been possible without the very precise calculations reported

in the present work.

In their very thorough study of the rovibronic levels of

BH2, Kolbuszewski et al.19 pointed out that “because of severe

resonances in the excited electronic state, a very accurate

potential energy surface will be needed for that state and for the

ground state in order to obtain term values that agree precisely

with the experimental results.” These perturbations occur both

between levels of the A state and by Renner interactions

FIG. 7. Differences between calculated and observed energy levels of 11BH2

(see Table I) for increasing levels of accuracy of the ab initio PESs. See the

text for further explanations of the meaning of the various acronyms.

of excited state levels with nearby ground state levels. In

particular, the authors found that the calculated A state (0,10,0)

and (0,12,0)Π levels of the various BH2 isotopologues differed

from experiment15 by 26–43 cm−1 due to such resonances.

By this criterion, the potential energy surfaces obtained in

the present work must be very accurate indeed, as these

differences between theory and experiment have been reduced

to a matter of a few cm−1. Furthermore, the sensitivity of the

LIF experiments has allowed us to identify transitions to three

perturbed ground state levels [(0,13,0) of 11BH2 and 10BH2 and

(0,16,0) of 11BD2] whose locations are precisely pinpointed by

the calculations. The present data probe regions of the excited

state potential of 11BH2 from 11 717 cm−1 to 21 000 cm−1,

more than 9200 cm−1, spanning ten bending levels and the

five stretch-bend combination levels from (1,10,0) to (1,14,0).

It is very gratifying that the calculated energy levels are in

excellent agreement with experiment throughout this whole

range (Table I and Fig. 7), illustrating once again the power

of very high level ab initio theory to provide very reliable

potential energy surfaces.

VI. CONCLUSIONS

In the present work, the LIF spectra of BH2 and its various

isotopologues have been obtained for the first time. These

data have greatly expanded the range of observed excited state

vibronic energy levels, from five bending levels of 11BH2 in

the pioneering work of Herzberg and Johns15 to 15 in the

present work, including ten bending levels and five stretch-

bend combinations. We have also observed many more levels

of 10BH2,11BD2, and 10BD2, yielding a very comprehensive

data set for testing the results of our very high level ab initiocalculations of the potential energy surfaces and variational

prediction of the rovibronic energy levels. High resolution

studies of the spectrum of 11BD2 allowed us to determine of

the ground state r0 structure of BH2 as r(BH) = 1.197(2) Å,

θ = 129.6(2)◦.In order to predict the excited state energy levels to an

accuracy within a few cm−1, it was found necessary to include

corrections for core correlation, extrapolation to the com-

plete basis set limit, electron correlation beyond CCSD(T),



and diagonal Born-Oppenheimer effects to the original

CCSD(T)/aug-cc-pV5Z potential energies. The resulting

potentials, without any empirical adjustment or fitting to

experimental data, gave excellent agreement with experiment,

including perturbed levels and even allowed the assignment of

a few transitions to high vibrational levels of the ground state

that gained intensity by Renner-Teller mixing with the excited

state.

ACKNOWLEDGMENTS

The research of the Clouthier group was supported by the

National Science Foundation. We are grateful to Dr. Bing Jin

for recording a few of the BH2 spectra. R.T. acknowledges

financial support from the Università of Bologna.

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bh 2 revisited: new, extensive measurements of laser

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